SMART Designs for Personalized Medicine

hello everyone thank you for the
opportunity to make this presentation today I will talk about sequential
multiple assignment randomized trial with a short name SMART trial this is a
novel clinical trial design for compare multiple adaptive intervention and we
introduced the concept give several examples and talk about methods to
design and analyzing this trial so the concept of personalized medicine is an
increasing popular topic into this healthcare research individualizing
patient care is particularly important in managing chronic diseases the patient
care in chronic disease typically take a long period of time during which
multiple clinical factors vary across different patient at a different time
within the same patient these clinical factors can be medication adherence, side
effects, intermediate response, and a history of previous treatment patient
received in early of the period the key to success in managing chronic disease
is to design a flexible treatment strategy that can adapt to patients
personal information for example we need a strategy to help adjust the inherent
heterogeneity across different patient and help control the variability within
the patient across time ideally the strategy should be able to help us
improve the individual compliance to the treatment patient receive and minimize
the burden and cost so this kind of study strategy fits the paradigm of
personalized medicine the chronical disease, the clinical practice of chronical
disease, such as cancer care and depression management clinician
often need to make a sequence of treatment decision
throughout the entire course of patient clinical care
this decision usually adapt to a patient’s treatment and a covariant
history in previous stage in the same treatment so adaptive intervention formalizes
mechanic of such a sequence of decision-making here is an example of
two-stage adaptive intervention designed for a newly diagnosed patient with the
Diffuse Large B-Cell Lymphoma this is originally reported by Habermann in 2006
and published in JCO. under this adaptive intervention, patient was first given
CHOP: a combination of four chemotherapy agent for eight cycles at
stage one, at the end of stage one, the patients will classify as responders and
non-responders here response is defined as complete remission or partial
remission and non-response otherwise for now responders they will be given
Rituximab, they were given G-CSF for supportive at the stage two and for
responders they will give Rituximab for six months as a maintanence this is one
adaptive intervention and an intervention can be recommended to all
the patient with newly diagnosed Diffuse Large B-Cell Lymphoma
a patient under this adaptive intervention in clinical practice can
possibly receive two treatment sequence one is CHOP-Response
Rituximab and the other is CHOP-No Response
G-CSF specifically which treatment sequence a patient will follow in
practice depending on value of intermediate response observed on this
patient. The adaptive intervention typically has four important components.
first it has multiple treatment stage each treatment stage refers to an
interval of time during which a patient receive one specific treatment for
example in this case we can see at a stage one, all the patient will receive
one treatment which is CHOP while at the stage two a part of the patients
will receive Rituximab and rest of them receive G-CSF
in the practice researchers can define a number of stage
of adaptive intervention depending on a feature of patient care and interests of
study also an adaptive intervention has a sequence of decisions regarding to the
treatment selection for example in this case at the stage two a decision needs
to be made is if a patient failed to respond at the end of stage one which
treatment should be selected for next stage well if the patient achieved
stabilized which main treatment should be selected for maintenance the stage one
treatment here is not adaptive to any baseline information for surely we can
design another adaptive decision at stage 1 for example we can give patient
with comorbidity a certain treatment and for those patients without comorbidity
another type of treatment in that case we’ll receive four treatment sequence in
this adaptive intervention which was more complicated also adaptive intervention
has a set of treatment option at a decision-making point so can choose
different treatment based on patients different clinical information this
option can be dose-type or timing of medication given to patient if there’s
only one treatment option then different patient based on different
clinical condition is not meaningful in adaptive intervention also we have
tailoring variable which is variable that contains
information to support the decision making in adaptive intervention for
example in this case the tailoring variable to the supported decision-making at the
stage two is the response to CHOP measure at the end of stage 1 so we
based on the patient’s response to decide which treatment we give to this
patient at the second stage a commonly seen kind of variable in adaptive
intervention include baseline covariates, previous treatments
side effect, and a medication adherence so we for the example I give in previous
slides and the four important components is easy to understand the official
concept of adaptive intervention here adaptive intervention it’s a multi stage
treatment strategy consisting of a sequence of decision-making rules one
per stage of intervention which is specifying how to adapt the treatment
selection according to individual patients clinical history of treatment
other covariates so statistics play important role in the
adaptive intervention research it provides the evidence base or we can call
this data-driven framework to help us optimize the decision-making for
treatment selection for individual in adaptive intervention also it help us
identify the optimal adaptive intervention leading to the best how
come in a long run. a natural question in adaptive intervention research is
whether or not an adaptive intervention identified in the study is
better than the others so in terms of statistics we can transfer the question
into whether a particular adaptive intervention can lead to a better
average outcome in the long run. to answer this question we can we need to
conduct a causal inference based on a sample data collect from study it can be
true type of study one is observational study and the other is randomized
clinical trial in observational study, the data is relatively easy to obtain
and with low cost however the reason that a patient received a specific
treatment in observational study it’s not always completely documented so the
conclusion made based on observational data sometimes can be biased potentially
unfortunately the existence of the impact from a measure confounded the
observational study is not numerically testable because we don’t even have the
data so we cannot conduct the test so the finding in observational study need
to be verified using the result of randomized clinical trial. in a
randomized clinical trial the reason that a patient was assigned a treatment is
because, is a result of randomization so the randomization
procedure can help us rule out the impact from a major confounder
so we can use the data directly to support the causal inference. today’s
presentation we talked about the design for randomized clinical trial. sequential
multiple assignment randomized trial with a short name SMART
trial is a clinical trial design that can be used to compare multiple adaptive
intervention such a design randomly assign patients to a collection of adaptive
intervention that may overlap in terms of treatment decision so by the virtue of
randomization this design provided information allow us to compare multiple
adaptive intervention directly in a study you can see here is an example of
two-stage SMART for those being former patient. under this design pressure
who enroll in the trial will first randomized to receive CHOP or R-CHOP
which is Rituximab-CHOP for eight cycles at stage one. at the end of stage
one the intermediate evaluation was given to each patient and the patient
will classify as responders and non-responders
based on the definition we mentioned in previous slides. for non-responders in
this study at the stage two they all given G-CSF
for supportive while for those responders they will be randomized again to receive
Rituximab or observation for maintenance at stage 2 we can see there are six
treatment sequence embedded in this design diagram presented as the arrow goes
from left to the right and we denote it by sequence A, B, C to F. for example sequence
A is CHOP response Rituximab so a patient
who complete this trial will follow one of this six treatment sequence depending
on the result of randomization and intermediate response. the previous
example of two stage at active intervention is highlighted in red in
this design diagram by which we give patient CHOP at the stage one, Rituximab
at the stage two if the patient respond and a G-CSF at the stage two
if the patient fail to respond so we denote this adaptive intervention
as (A+C) here because it consists to treatment sequence, sequence
A and sequence C. similarly we can identify another three adaptive
intervention in this design diagram each adaptive intervention consists twp
treatment sequences one for response and one for no response and both treatment
sequence share the same stage one treatment. for example we
can identify another adaptive intervention by giving people CHOP at stage one,
observation at stage 2 if the patient respond and G-CSF
at stage 2 if a patient fail to respond if you look at the design diagram
we can see both these two adaptive strategy, they actually share the same
treatment sequence which was sequence C here so that is to say for those
patient who receive CHOP at the stage one fail to respond and receive G-CSF at
the stage two actually contributed information that helped us to evaluate
two adaptive intervention. this feature makes SMART a very efficient design but
also introduced some complicity in statistical inference and we talked more
detail about it the curse of dimensionality is the major concern of
SMART design because the total number of adaptive intervention identified in
SMART increase exponentially as the number of
treatment option and intermediate response categories increases for example in this
study we can identify for adaptive
interventions however we will modify this a little bit we increase one
treatment option for those patient who fail to respond to stage one treatment
so the total number of intervention will increase immediately from four to eight
which is substantial. this feature has big impact in a statistical inference in
terms of control of false positive finding and I will talk more about it so
in a clinical trial practice there are some other clinical designs more or less
to share some common feature with SMART the similarity between SMART designs and
these designs sometimes cost confusion for clinical trialists
who gets to know this concept at the beginning these are also the playground
that we statisticians receive a lot of questions from our clinician and
collaborators. today I will compare SMART design with two clinical trial designs:
crossover and adaptive design so by making these comparisons we further
demonstrate the feature of SMRT designs here. so first we look at a crossover
design which is a repeated measure randomized clinical trial design that
each individual in this study will receive variant treatment sequence
across multiple stage here is an example of crossover study compared two fixed
treatment A and B at the beginning of stage one patients were randomized to
receive A or B at the stage one. at the end of stage one the primary outcome was
measure for each patient and then patients with switch from A to B from B
to A at the stage two and repeat a same story at the second stage so
operationally crossover design is somewhat similar to SMART because in
this design patients also receive different treatments across multiple
stage however we can clearly separate these two designs from three aspects so
first of all crossover design is motivated by improved efficiency and
reduce the total sample of the study but the goal is still try to compare two fixed
treatments We can call this two non-adaptive
intervention for example in this case although different patients receive
treatment sequence of A to B or B to A this design is just try to take two measures
from each patient and the goal is to reduce the total sample size by still with
their primary hypothesis to compare treatment A and B however the SMART is
designed to compare multiple adaptive intervention which is different from
crossover also in a crossover design the treatment assignment only depends on the
baseline style randomization in this case patients either received treatments A to B
or sequence B to A but which sequence the patient will follow completely
depends on the baseline randomization once the trial is star will never change
it unless the patient drop out however in a SMART the story is totally different
only the set of decision rules about how to
assing treatment is pre-specified at the baseline because the randomization
is conducted sequentially at the beginning of every stage so until the
last decision is made is unlikely to know each patient follow what kind of
treatment sequence so also the major pitfall of crossover design is something
called carryover effects which is the prior effect of treatment A or B can be
confounded with the succeeding treatment effect of B or A so in this case if the
carryover effect exists so when we look at the primary outcome at
the end of stage two we won’t be able to know if the primary outcome is
purely because the treatment patient received at the stage two or is partly
because treatment a patient received at the
first stage which is reduced the power of the study so to avoid the
contamination of carryover effect in a crossover design the typically insert a
unique component called wash over a period between two two treatment stage
the key to set up a wash over period is to control the time
window large enough to eliminate any possible carryover effects on the other
hand in order to make the trial efficient once this requires is made we
also need to try to control the time window as short as possible. in a SMART
is different because the SMART design is trying to compare the effects of adaptive
intervention and the effect of adaptive invention is possibly due to the
interaction effect between the treatment a patient received in different stage so
in SMART we do not set up any washout period to try to rule out the carryover
effects another term that sometimes get confused with SMART is adaptive design
in fact adaptive design is an umbrella term that covers a family of randomized
clinical trial. the members in the family including continuously assessment design,
sample size recalculation design, or adaptive randomization design all this
design has one common feature which is they try to modify some of the design
aspects such as total sample size randomization scheme based on the result
of interim analysis the goal of this adaptive design is trying to improve the
overall quality of patient care in favor of those treatment to show better
evidence of better efficacy or less toxicity from the interim analysis so
the between subject information is adaptive while in a SMART what we adapt
is with-in subject information between different stage but a common design
element like total sample size randomization scheme are all fixed we do not
change it once the study is start so after introduced the concept of
adaptive intervention and SMART trial next I will talk about methods to
design SMART and analyzing SMART data first I will talk about how to estimate
the adaptive intervention value with two methods such as maximum likelihood estimator
and inverse probability weighting estimator
then I will talk about how to conduct the hypothesis test in SMART to compare
multiple adaptive intervention I will talk about pairwise test also global test or
call omnibus test then I will talk about how to conduct the sample size
calculation in designing a SMART trial so before the illustrative method, first let’s
take a look at the general scheme of two stage SMART this is the scheme that we
used to conduct the statistical inference. Patient
enrolled in the trial was first randomized to any treatment option at stage one, we denoted
by T1, T2 to Ti for each stage one treatment the certain number of
intermediate response categories follow it in a general SMART design we allow the number
of intermediate response categories to vary by different stage
one treatment for example under T1 where J1 intermediate response
categories Denoted by R11, R12 to R1j1
while under Ti we have ji intermediate response categories denoted by our Ri1, Ri2 to
Riji similarly where are the number of stage 2 treatment option can be varied
by different history of stage 1 treatment and intermediate response
suppose a patient enroll in the trial received T1 at the stage 1 and had intermediate
response R11 at the stage two based on this design patient will be
randomized to receive one out of K11 treatment option denoted by S111,
S112 to S11K11 here. so in the lymphoma trial I just talked
about we have two treatment option at stage 1 so T1 will be CHOP and T2
will be R-CHOP because we defined the intermediate response for both stage 1
treatment as a binary outcome so after T1 we’ll have 2 bullets here with R11 which
represent the response and R12 will represent no response
similarly after T2, we have two bullets with R21 corresponding to
response and R22 responding to no response for the stage-two treatment
because we do not randomized non-responders again
so following R12 and R22 we’ll have one bullet of treatment option
while for those responders who will be randomized to two treatment option so we
have two bullets here following along one and another two bullets for R21
so data collected from the general scheme of two-stage SMART for a patient
can be summarized as a longitudinal trajectory across time (U,X,V,Y) where U is
the variable represent the stage one treatment, X is the intermediate
response, V is the stage two treatment and Y is the final primary outcome so to
do the statistical inference we assume (U,X,V,Y) are independent and
identically distributed with pi_i being the stage one randomization
probability corresponding to the patient received TI at the stage one. p_ij is the
intermediate response rate corresponding to R_ij given a patient received Ti at
the stage one and pi_ijk being the stage two randomization probability
corresponding to a patient receive S_ijk at a stage 2 given a patient received
TI the stage 1 had an intermediate response R_ij. finally we’ll see why the
primary outcome of interest follow given a history of Ti, R_ij, S_ijk follow a
distribution with mu_ijk in the parameter of interest and a tau_ijk being a
nuisance parameter so specifically in this presentation we just concern we just
focus on the mean of primary outcome as a parameter of interest
Suppose the primary outcome is a continuous variable Y given history of Ti, R_ij, S_ijk
will follow a normal distribution with mu_ijk being the mean of
primary outcome which is the parameter of interest and variance sigma_ijk squared.
so under this framework each adaptive intervention consists a series of
treatment sequences with each of the sequence there’s a specific mean of
primary outcome corresponding to it and we denote it by mu all these sequence
share the same stage one treatment we define the value of adaptive intervention
as a weighted sum of this treatment sequence specific mean mu weighted by
the intermediate response rate P so value of adaptive intervention can be
interpreted as the average primary outcome across all the possible
treatment a patient can receive under the adaptive intervention now let’s take
a look at the lymphoma trial example suppose we are interested in
calculate the value for adaptive intervention A plus C we have two treatment
sequence here sequence A and C so have two sequence specific mean denoted by mu_A
and mu_C let P1 be the intermediate response rate following CHOP so the value of
adaptive intervention A plus C can be calculated by P1 which is the
probability that we will observe a patient who following sequence A under
this adaptive intervention multiply the mean of sequence mu_A plus 1 minus P1
which is the probability that we observe a patient following sequence C under
this adaptive intervention multiplied by mu_C similarly we can calculate the
value of other three adaptive intervention as we show in the bottom of
these slides. to estimate a value of adaptive intervention we can use maximum
likelihood estimator MLE the MLE of theta adaptive intervention
value can be obtained by plugging the MLE of those intermediate response rate
P and MLE of of sequence-specific mean mu. the MLS of P and mu can be
obtained by maximizing the joint distribution of (U,X,V,Y). alternatively we
can use another method to estimate the value of adaptive intervention this is
inverse probability weighted estimator using formula one in the top of the
slide. here W is the inverse probability treatment ways assigned to each patient
following complete SMART trial where l is the observed primary outcome
observed in patient l. l is the indicator of each subject who complete a SMART
trial with value 1 to n and it’s the total number of patient who completed the
trial to build the inverse probability treatment weights for those patient who
follow a sequence not belonging to the adaptive intervention of interest we
similarly give this patient a weight of 0 while for those patient who follow a
sequence belonging to the adaptive intervention we’re interesting in the
weight can be built based on a cumulative product of inverse randomization
probability corresponding to all the treatment a patient received in the
study formula 3 is the formula to calculate
the variance estimator of a IPWE we can see this is a function of M total sample
size, W inverse probability treatment weight and Y observe primary outcome so let’s
go through the lymphoma trial and see how we construct the weights to calculate
the inverse probability weighted estimator
suppose we’re interesting in the adaptive innovation A+C we have three
randomization probability here pi_1 corresponding to CHOP at the stage 1
pi_2 corresponding to Rituximab for those responders of CHOP and pi_3
corresponding to the Rituximab corresponding to those R-CHOP
pi_1 and pi_2 will be related to calculate the weights for those patient who
following adaptive intervention A+C For patient who follow sequence A here
they had two randomization in the study one in stage 1 and one in stage two so
the weight can be calculated using one over pi_1 multiply 1 over pi_2 to
make it simple, let’s assume pi_1, pi_2 and pi_3 are all equal to 50% so the weights for
those patient who follow treatment sequence A equal to 4 for those
patients who follow treatment sequence C the only randomization happens at the
beginning of stage 1 so for this patient the weight can be calculated by 1 over
Pi_1 which is 2 while for those patient who follow other treatment sequence not
belonging to this adaptive intervention B, D, E and F we simply give them weight
of 0 and then we plug in the formula can calculate the IPWE. so these two methods
to estimate the adaptive intervention value makes more likely estimator and
inverse probability weighting estimator they both consistent estimator and
asymptotically identical so when a sample size of a SMART is large enough
they have the same performance or at least similar performance compared to
the maximum likelihood estimator the calculation of IPW is relatively simple
because we can see the function only involve two components the randomization
probability and the observe primary outcome at the end of the study so we do not
have to deal with the complex structure of SMART also this method is robust to
the assumption of data distribution on the other hand the maximum likelihood
estimator take the advantage of asymptotic
efficiency when the assumption about data distribution correctly referred the
feature of sample data on the other hand if the assumption
about the distribution do not correctly reflect the feature of sample data that
the performance will go to the opposite way so I’ve done a lot of study in this
field and gained a lot of experience from the simulation study for SMART design
with moderate sample size where the primary outcome is continuous variable
or binary variable we can feel comfortable about the maximum likelihood
estimator and use this one so we take the advantage of asymptotic
efficiency so next I will talk a little about the distribution about MLEs which
is the fundamental theory of the statistical inference for comparison
here the upper case theta is the vector of all adaptive intervention value
embedded in a SMART design the lower case theta is a single adaptive intervention
value the subscript of theta is the indicator of each adaptive intervention
and G is the total number of adaptive intervention can be identified in a
SMART design so it can be pooled that the MLE of theta follow a multivariate
normal distribution asymptotically with variance covariance matrix sigma.
Sigma here is a block diagonal matrix of a series of small covariance matrix
denoted by Sigma_1, Sigma_2, to Sigma_i each of these small covariance matrix
corresponding to the MLEs of those adaptive intervention value share the same
stage 1 treatment in the study for example Sigma_1 here is the covariance
matrix of MLEs of all the adaptive intervention
starting with T1 at stage 1 these MLEs are correlated to each other due to the
overlap in structure and the correlation varies by study design. to compare
multiple adaptive intervention we can use a pairwise comparison by which we
conduct a series of pairwise tests to compare each pair of the adaptive
interventions the null hypothesis of pairwise test is
two adaptive interventions have the same value we can use formula four to
calculate the test statistics of a pairwise test here for denominator we
can plug in the estimator of adaptive intervention of two adaptive
interventions it can be a MLE or can be inverse probability weighted estimator
so for illustration purpose to make it simple for now I just focus on maximum
likelihood estimator. to calculate the variance, the denominator, if we
trying to compare two adaptive intervention do not overlap with each other in
structure the calculation is relatively easy because it only involve the
variance components when we try to compare two adaptive intervention there
are some more overlap in the design structure then the
computation will be a little more complicated because you need to involve
the cross product which is the covariance all this variance and
covariance information can be obtained from the estimate Sigma here so next I
will use a real data example to illustrate how we conduct the pairwise
comparison the data was collected the data was actually from a study called
CODIACS:comparison of depression intervention after accurate coronary
syndrome. this is a study that aimed to assess the quality of depression care of
different management program so the primary outcome of the study is
Beck Depression Inventory which is a continuous score, a higher
level of that Beck Depression Inventory indicating a more severity of depression
so an adaptive intervention relates to a more BDI reduction from baseline
indicating a better treatment effects so this is the design diagram of the study at
the stage one patient were randomized to receive medication and a behavioral
therapy for two months at the end of stage one patient were classified as
responders and non-responders based on the
reduction of BDI from baseline greater than three or no and then they will be
randomized again to receive medication and behavior therapy for another four
months based on different history of stage one treatment and intermediate
response this design structure provide data that allow us to evaluate up to
eight adaptive intervention. first we calculate the estimated adaptive
intervention to estimate the intervention value first we need to
estimate the response rate first we will estimate an intermediate
response rate following medication and behavioral therapy then we need to
calculate the sequence mean following each of those sequence then we plug in
the formula and calculate the MLE of all eight adaptive intervention as we
show here we can see the fifth adaptive intervention has the largest MLE so
we call this observed the best adaptive intervention. for the variance-covariance
matrix because we have eight adaptive intervention here this is actually a
block diagonal matrix with dimension eight by eight the small covariance matrix in
the upper left is the covariance matrix of those MLEs corresponding to the
intervention following medication at the stage one and then we have another four
adaptive intervention following behavioral therapy and variance
covariance matrix on the bottom right so a potential issue of using
pairwise comparison to evaluate all the adaptive innovation in SMART is this
procedure need to take into account multiple comparison issue
you see methods such as Bonferroni correction which is known to be
conservative when a number of adaptive intervention can be identified in SMART
increase for example in this case we can see suppose we try to compare the
adaptive intervention control overall significant level at 0.05 because
we have eight adaptive intervention so a pairwise comparison with Bonferroni
correction require a p-value less than 0.0018 to gain overall
significant. The last column of this table
give us all the p-values of pairwise tests to compare each adaptive
intervention with observed best which adaptive intervention five so you can
see but a comparison although there’s one p-value less than 0.05
after Bonferroni correction we cannot claim overall significant because there are
too many adaptive interventions this problem is particularly significant in
SMART because the sequential randomization of SMART always generate a
high dimensional data that are including a lot of adaptive interventions so
alternatively we can use a gatekeeping approach to do the analysis. A gatekeeping
approach is two-step approach in step one we conduct a global test or
sometime we call this omnibus test with the null hypothesis the older adaptive
intervention have the same value only if the
null hypothesis of the omnibus test was rejected we move
forward to do a selection otherwise we stop analysis a claim there’s no more
significant so here is the formula five is how we calculate the test statistics
Q for this global test and it’s the total sample size of patient who
complete SMART trial. C is the contrast matrix and I will talk about this later how
to construct it. Theta hat is the estimated value of all the adaptive intervention
and the Sigma hat is to estimate the asymptotic covariance matrix under the
null hypothesis, Q the test statistics will follow a chi square
distribution with the degrees of with a nu while under the alternative
hypothesis Q follow a non-central chi square distribution with
the non-centrality parameter lambda star the degrees of freedom of chi squared
test can be calculated using
formula 6 here summation of K_ij is the total number of stage 2 treatment
option and the summation J_i is the total number of intermediary response
categories. i is the total number of stage one treatment option let’s use the
example of CODIAC to see how we conduct a global test we have eight adaptive
intervention in this study so the null hypothesis of the global test is all
eight adaptive intervention have the same value to calculate the test
statistics first we need to construct the contrast matrix because we have
eight adaptive intervention the dimension of this contrast will be seven
by eight with each column of the matrix corresponding to one specific adaptive
intervention each row of this contrast each row of this contrast matrix
corresponding to one contrast to compare a pair of adaptive intervention in the
first row we compare adaptive intervention one versus intervention two in the
second row we compare intervention one with intervention three etc. once we have the contrast matrix we plug
in the formula with total sample size and estimated adaptive intervention
Theta hat and estimating asymptotic covariance matrix we can
calculate the test statistic Q equal to 36 to calculate the degrees of freedom
let’s go back to the design structure here we have eight treatment option at the
stage two, four intermediate response categories two stage one treatment
option so the degrees of freedom equal to 8 minus 4 plus 2 minus 1 which is
equal to 5 by this means we finally obtain a
p-value of global test less than 0.001 because it’s
more powerful than pairwise tests and we can claim overall significant in this
study. another good thing about the global test is a provide efficient
method that can help us power a SMART trial here is the general approach to
conduct the sample size calculation for SMART trial to conduct the sample size
calculation first we need to specify with the designd structure statistician
communicate with clinical collaborators and if our finalized the design
structure what will be the treatment option at the stage one in a stage two
how to define the intermediate response and then we need to set up the
randomization probability ties once we finalize the design structure we need to
obtain lambda star which is the non centrality parameter and
other alternative hypotheses in step two to obtain the value of lambda star we
need to solve the equation of seven to do this with the pre-specified the
target type one error rate alpha and target power minus beta and then we need
to calculate the effect signs Delta using formula eight here C is the contrast
matrix we just saw. Theta star is the target adaptive
intervention value and a sigma star is the target asymptotic variance covariance
matrix once you have the value of lambda star and the Delta we divide the lambda
star by Delta we can obtain n which is the total sample size of all the
patients who we require for SMART trial another good thing about
SMART trial is other than it is a very efficient a design for comparing
multiple adaptive intervention the study design also provide a very rich
information that allow to answer a series
of secondary research question for example in this study the Lymphoma
Trial, the primary interest question is compare four adaptive intervention but
we can also use the data to compare CHOP and R-CHOP to see which one provides a
better response rate for the patient with newly diagnosed lymphoma also we
can compare Rituximab vs. observation for those responders of CHOP and compare
Rituximab and observation for those responders after R-CHOP we
can do this is because we conduct sequential randomization given different
conditions of the patients sequentially in the study
although the trial was powered based on the primary question so when we study
this secondary question we may not have enough power to control the study under
a very restrict of the type of one error
however we also still provided a very rich valuable information for those
questions this is another example that we use SMART design to improve the
design efficiency compared to a traditional randomized clinical trial
because the time of limit I will skip this one if anyone who is interested in
it you can contact me after the presentation and I will very pleased to
talk about it so in summary SMART is efficient randomized clinical trial
design that provide data to compare multiple adaptive interventions also
other than answering primary question it also provides rich information to answer
a series of secondary question in terms of patient care of chronic disease in
statistics in the last 10 years many study has been conducted in this field
and several important paper has been published so the technique for design in
a SMART trial and analyzing SMART data is getting mature so it will be a good
time to conduct this clinical trial design in the clinical practice of
medical research so it has a broad application potentially in the future
these are the reference of today’s presentation. thank you

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